Rapid and Stable Flood Inundation Modelling Using the Local Inertial Equation

Abstract

 A new formulation of the St. Venant momentum equation, the local inertial equation, was developed recently at the University of Bristol for stable and fast flood inundation modelling. The local inertial term of the momentum equation, which is neglected in the diffusive wave approximation, is additionally considered in the local inertial equation. Herein we demonstrate the manner in which flood inundation simulations can be stabilized by adding the local inertial term using mathematical stability analysis and numerical simulations. Mathematical stability analysis suggests the following two characteristics of the local inertial equation as important for computational efficiency: 1) time evolution of flood inundation is solvable explicitly using semi-implicit approximation of the discharge term in the Manning’s roughness equation; and 2) the type of the governing partial differential equations changes from a parabolic system to a hyperbolic system by adding the local inertial term to the diffusive wave equation. Both mathematical analysis and numerical simulations revealed that the local inertial equation is more computationally efficient than the diffusive wave equation, especially in cases of high- resolution inundation flood modelling in very flat regions.